PenPC: A two-step approach to estimate the skeletons of high-dimensional directed acyclic graphs.

Estimation of the skeleton of a directed acyclic graph (DAG) is of great importance for understanding the underlying DAG and causal effects can be assessed from the skeleton when the DAG is not identifiable. We propose a novel method named PenPC to estimate the skeleton of a high-dimensional DAG by a two-step approach. We first estimate the nonzero entries of a concentration matrix using penalized regression, and then fix the difference between the concentration matrix and the skeleton by evaluating a set of conditional independence hypotheses. For high-dimensional problems where the number of vertices p is in polynomial or exponential scale of sample size n, we study the asymptotic property of PenPC on two types of graphs: traditional random graphs where all the vertices have the same expected number of neighbors, and scale-free graphs where a few vertices may have a large number of neighbors. As illustrated by extensive simulations and applications on gene expression data of cancer patients, PenPC has higher sensitivity and specificity than the state-of-the-art method, the PC-stable algorithm.

Exact analytical expressions for the potential of electrical double layer interactions for a sphere-plate system.

Exact, closed-form analytical expressions are presented for evaluating the potential energy of electrical double layer (EDL) interactions between a sphere and an infinite flat plate for three different types of interactions: constant potential, constant charge, and an intermediate case as given by the linear superposition approximation (LSA). By taking advantage of the simpler sphere-plate geometry, simplifying assumptions used in the original Derjaguin approximation (DA) for sphere-sphere interaction are avoided, yielding expressions that are more accurate and applicable over the full range of κa. These analytical expressions are significant improvements over the existing equations in the literature that are valid only for large κa because the new equations facilitate the modeling of EDL interactions between nanoscale particles and surfaces over a wide range of ionic strength.

Intake, digestibility, and passage of a commercially designed diet by two Propithecus species.

The digestibility and passage of an experimental diet was used to compare the digestive physiology of two Propithecus species: P. verreauxi and P. tattersalli. Though both animals have a similar feeding ecology, the captive status of P. verreauxi is considered more stable than that of P. tattersalli. The test diet included a local tree species, Rhus copallina, at 15% of dry matter intake (DMI) and Mazuri Leafeater Primate Diet at 85% of DMI. The chemical composition of the diet (dry matter basis) was 25% crude protein, 34% neutral detergent fiber (NDF), and 22% acid detergent fiber (ADF) with a gross energy of 4.52 kcal/g. After a 6 week acclimation to the experimental diet, animals were placed in research caging. After a 7 day adjustment period, animals were dosed with chromium mordant and Co-EDTA as markers for digesta passage and all feed refusals and feces were collected at timed intervals for 7 days. Digestibility values, similar for both species, were approximately 65% for dry matter, crude protein, and energy, and 40% and 35% respectively, for NDF and ADF. Transit times (17-18.5 hr) and mean retention times (31-34 hr) were not significantly different between species, and there was no difference between the chromium mordant and Co-EDTA. Serum values for glucose, urea, and non-esterified fatty acids (NEFA) were obtained during four different time periods to monitor nutritional status. While there was no change in serum glucose, serum urea increased over time. The NEFAs increased across all four time periods for P. verreauxi and increased for the first three periods then decreased in the last period for P. tattersalli. Results obtained indicate no difference in digestibility nor digesta passage between species, and that both Propithecus species were similar to other post-gastric folivores.

Electrostatic Energetics of Bacillus subtilis Ribonuclease P Protein Determined by Nuclear Magnetic Resonance-Based Histidine pKa Measurements.

The pKa values of ionizable groups in proteins report the free energy of site-specific proton binding and provide a direct means of studying pH-dependent stability. We measured histidine pKa values (H3, H22, and H105) in the unfolded (U), intermediate (I), and sulfate-bound folded (F) states of RNase P protein, using an efficient and accurate nuclear magnetic resonance-monitored titration approach that utilizes internal reference compounds and a parametric fitting method. The three histidines in the sulfate-bound folded protein have pKa values depressed by 0.21 ± 0.01, 0.49 ± 0.01, and 1.00 ± 0.01 units, respectively, relative to that of the model compound N-acetyl-l-histidine methylamide. In the unliganded and unfolded protein, the pKa values are depressed relative to that of the model compound by 0.73 ± 0.02, 0.45 ± 0.02, and 0.68 ± 0.02 units, respectively. Above pH 5.5, H22 displays a separate resonance, which we have assigned to I, whose apparent pKa value is depressed by 1.03 ± 0.25 units, which is ∼0.5 units more than in either U or F. The depressed pKa values we observe are consistent with repulsive interactions between protonated histidine side chains and the net positive charge of the protein. However, the pKa differences between F and U are small for all three histidines, and they have little ionic strength dependence in F. Taken together, these observations suggest that unfavorable electrostatics alone do not account for the fact that RNase P protein is intrinsically unfolded in the absence of ligand. Multiple factors encoded in the P protein sequence account for its IUP property, which may play an important role in its function.

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally- derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.